alberto pliego marugán 1, fausto pedro garcía márquez 1,...acyclic graph is a directed graph,...

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Article

Optimal Maintenance Management of OffshoreWind FarmsAlberto Pliego Marugán 1, Fausto Pedro García Márquez 1,* and Jesús María Pinar Pérez 2

Received: 30 October 2015; Accepted: 24 December 2015; Published: 15 January 2016Academic Editor: Frede Blaabjerg

1 Ingenium Research Group, Universidad Castilla-La Mancha, 13071 Ciudad Real, Spain;[email protected]

2 CUNEF-Ingenium, Colegio Universitario de Estudios Financieros, 28040 Madrid, Spain;[email protected]

* Correspondence: [email protected]; Tel.: +34-926-295300 (ext. 6230)

Abstract: Nowadays offshore wind energy is the renewable energy source with the highest growth.Offshore wind farms are composed of large and complex wind turbines, requiring a high levelof reliability, availability, maintainability and safety (RAMS). Firms are employing robust remotecondition monitoring systems in order to improve RAMS, considering the difficulty to access thewind farm. The main objective of this research work is to optimise the maintenance management ofwind farms through the fault probability of each wind turbine. The probability has been calculatedby Fault Tree Analysis (FTA) employing the Binary Decision Diagram (BDD) in order to reduce thecomputational cost. The fault tree presented in this paper has been designed and validated basedon qualitative data from the literature and expert from important European collaborative researchprojects. The basic events of the fault tree have been prioritized employing the criticality methodin order to use resources efficiently. Exogenous variables, e.g., weather conditions, have been alsoconsidered in this research work. The results provided by the dynamic probability of failure and theimportance measures have been employed to develop a scheduled maintenance that contributes toimprove the decision making and, consequently, to reduce the maintenance costs.

Keywords: offshore; wind turbines; maintenance management; fault tree analysis; binarydecision diagrams

1. Introduction

The renewable energy industry is in continuous development to achieve the energy frameworktargets established by governments [1]. Nowadays, the most developed countries are focused onimproving the technology for offshore wind energy. The main advantages of the offshore wind farmsare [2]:

- The wind power captured by wind turbines (WTs) is more than onshore.- The size of offshore wind farms can be larger than onshore.- The environmental impact for offshore is less than in onshore.

The main disadvantages are:

- It is more complex to evaluate the wind characteristics.- Larger investment costs. The offshore installation cost is 1.44 million €/MW, where the onshore

is 0.78 million €/MW [3].- Operation and maintenance (O & M) tasks are more complex and expensive than onshore. The

offshore O & M costs tasks are from 18% to 23% of the total system costs, being 12% for onshorewind farms [4].

Energies 2016, 9, 46; doi:10.3390/en9010046 www.mdpi.com/journal/energies

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Energies 2016, 9, 46 2 of 20

The objective of this paper is to develop a novel maintenance management approach in order toestablish a proper strategy for the maintenance task by using a predictive maintenance method basedon statistical studies. This approach provides information about the WTs with high fault probability, aranking of components of WTs to repair or replace according to the state of the system over the time,and when those maintenance tasks must be carried out. An adequate maintenance planning to ensurethe right operation of an offshore wind farm is required. For this purpose, different techniques andmethods of condition monitoring (CM) are employed for detection and diagnosis of faults of WTs [5].Most of the research papers consider the CM in WTs referred to blades [6], gearboxes [7], electrical orelectronic components [8] and tower [9]. CM leads to improve RAMS and to increase the productivityof wind farms.

2. CM Applied to WT

The main components of WTs are illustrated in Figure 1. WTs are usually three-blade units [10].Once the wind drives the blades, the energy is transmitted via the main shaft through the gearbox tothe generator. At the top of the tower, assembled on a base or foundation, the housing or nacelle ismounted and the alignment with the direction of the wind is controlled by a yaw system. There is apitch system in each blade. This mechanism controls the wind power and sometimes is employed asan aerodynamic brake. Finally, there is a meteorological unit that provides information about the wind(speed and direction) to the control system.

Energies 2016, 9, 46

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The objective of this paper is to develop a novel maintenance management approach in order to establish a proper strategy for the maintenance task by using a predictive maintenance method based on statistical studies. This approach provides information about the WTs with high fault probability, a ranking of components of WTs to repair or replace according to the state of the system over the time, and when those maintenance tasks must be carried out. An adequate maintenance planning to ensure the right operation of an offshore wind farm is required. For this purpose, different techniques and methods of condition monitoring (CM) are employed for detection and diagnosis of faults of WTs [5]. Most of the research papers consider the CM in WTs referred to blades [6], gearboxes [7], electrical or electronic components [8] and tower [9]. CM leads to improve RAMS and to increase the productivity of wind farms.

2. CM Applied to WT

The main components of WTs are illustrated in Figure 1. WTs are usually three‐blade units [10]. Once the wind drives the blades, the energy is transmitted via the main shaft through the gearbox to the generator. At the top of the tower, assembled on a base or foundation, the housing or nacelle is mounted and the alignment with the direction of the wind is controlled by a yaw system. There is a pitch system in each blade. This mechanism controls the wind power and sometimes is employed as an aerodynamic brake. Finally, there is a meteorological unit that provides information about the wind (speed and direction) to the control system.

Figure 1. Components of the wind turbine (WT) where: 1—pitch system; 2—hub; 3—main bearing; 4—low speed shaft; 5—gearbox; 6—high speed shaft; 7—brake system; 8—generator; 9—yaw system; 10—bedplate; 11—converter; 12—tower; 13—meteorological unit.

CM systems are composed of different types of sensors and signal processing equipment applied on the main components of WTs such as blades, gearboxes, generators, bearings and towers. The choice and location of the right type and number of sensors are a key factor. The acquisition of accurate data is critical to determine the occurrence of a fault and to address the solution to apply. Nowadays, different techniques are available for CM: vibration analysis [3,11], acoustic emission [3,12], ultrasonic testing techniques [13,14], oil analysis [15], thermography [3,13] and other methods [16].

The first step of the CM process is the choice of an adequate technique for data acquisition, including electronic signals with the measurement of the required conditions, e.g., sound, vibration, voltage, temperature, speed. Then, a correct signal processing method is applied, e.g., fast Fourier transform, wavelet transforms, hidden Markov models, statistical methods and trend analysis. Fault detection and diagnosis (FDD) involves both CM techniques and the signal processing methods.

Figure 1. Components of the wind turbine (WT) where: 1—pitch system; 2—hub; 3—main bearing;4—low speed shaft; 5—gearbox; 6—high speed shaft; 7—brake system; 8—generator; 9—yaw system;10—bedplate; 11—converter; 12—tower; 13—meteorological unit.

CM systems are composed of different types of sensors and signal processing equipment appliedon the main components of WTs such as blades, gearboxes, generators, bearings and towers. Thechoice and location of the right type and number of sensors are a key factor. The acquisition of accuratedata is critical to determine the occurrence of a fault and to address the solution to apply. Nowadays,different techniques are available for CM: vibration analysis [3,11], acoustic emission [3,12], ultrasonictesting techniques [13,14], oil analysis [15], thermography [3,13] and other methods [16].

The first step of the CM process is the choice of an adequate technique for data acquisition,including electronic signals with the measurement of the required conditions, e.g., sound, vibration,voltage, temperature, speed. Then, a correct signal processing method is applied, e.g., fast Fouriertransform, wavelet transforms, hidden Markov models, statistical methods and trend analysis. Faultdetection and diagnosis (FDD) involves both CM techniques and the signal processing methods.

The frequency of occurrence, i.e., the probability of failure, of an event is necessary to study inorder to improve the application of CMS for WTs [17]. This paper employed the Fault Tree Analysis(FTA) technique to calculate the probability of failure of the WT. FTA is a graphical representation oflogical relationships between events. A Binary Decision Diagram (BDD) has been used to provide an

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alternative to the traditional technique in order to reduce the computational cost. BDD is an approachthat determines the probability of failure of a system by examining the probability of failure of thecomponents. The BDD method does not analyses the FTA directly. The Boolean equation representsthe main event to analyse, e.g., the wind turbine failure, and it is obtained by BDDs that come from thefault tree. The ordering algorithm for the construction of the BDD has a crucial effect on its size, andtherefore the computational cost. The algorithms are heuristics, and this is the reason that in this paperhas been considered several in order to compare the results, being: Top-down-left-right, Depth FirstSearch, AND, Breath First Search, and Level.

Finally, in order to optimize the resources, e.g., human, material, economic resources, etc., properand accurate prioritization of the basic events, based on importance measurement, has been doneaccording to the criticality method [18]. The information provided by the aforementioned methodleads to establish an optimal maintenance management for offshore wind farms, considering bothendogenous and exogenous variables.

3. FTA and BDD

A Fault Tree (FT) is a graphical structure formed by the causes of a certain type of failure mode(Top Event) and the failure mode of the components (basic events) connected by logical operators suchas AND/OR gates [19]. The probability vector p represents the failure probabilities of the basic eventsqi, i P {1, . . . , n}, being n the total number of events [20,21].

Then, the system failure probability Qsys can be obtained via FTA according to q:

q “

¨

˚

˝

q1...

qn

˛

‹

‚

Complex systems analysis produce thousands of combinations of events (minimal cut sets) thatwould cause the failure of the system and are used in the calculation of Qsys [21]. The determinationof these minimal cut sets can be a large and time-consuming process, even on modern high speedcomputers. When the FT has many minimal cut sets, the determination of the exact failure probabilityof the top event also requires a high calculation costs. For many complex FTs, this requirement may bebeyond the capability of the available computers. Therefore, some approximation techniques havebeen introduced with a loss of accuracy.

The BDD method does not analyze the FT directly. The conversion of the FT to a BDD makepossible to calculate the probability of the top event by determining the Boolean equation of the topevent. The conversion process from FT to BDD presents several problems, e.g., the ordering schemechosen for the construction of the BDD has a crucial effect on its resulting size. A wrong orderingscheme may result in large BDD that presents high computational costs [19]. In order to improvethe resource deployment in an existing system, proper and accurate ranking of the basic events isnecessary [23,24]. Some prioritizations of the basic events of the FT have been considered in this paper.For further details of FTA and ranking methods, consultation of references [18,25] is recommended.BDDs have been successfully used in the literature as an efficient way to simulate FTs. BDDs wereintroduced by Lee [26], and further popularized by Akers [27], Moret [25] and Bryant [22]. Thesedecision diagrams are composed by a data structure that can represent a Boolean function [28].

A BDD is a directed acyclic graph representation (V, N), with vertex set V and index set N, of aBoolean function where equivalent Boolean sub-expressions are uniquely represented [29]. A directedacyclic graph is a directed graph, i.e., to each vertex v there is no possible directed path that starts andfinishes in v. It is composed of some interconnected nodes with two vertices. Each vertex is possible tobe a terminal or non-terminal vertex. Each single variable has two branches: 0-branch corresponds tothe cases where the variable has not occur and it is graphically represented by a dashed line (Figure 2);on the other hand, 1-branch cases are those where the event is being carried out and corresponds to

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the occurrence of the variable, and it is represented by a solid line (Figure 2). It allows to obtain ananalytical expression depending on the probability of failure of the basic events and the topology ofthe FT. Paths starting from the top event to a terminal 1 provide a state in which the top event willoccur. These paths are named cut sets.


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carried out and corresponds to the occurrence of the variable, and it is represented by a solid line (Figure 2). It allows to obtain an analytical expression depending on the probability of failure of the basic events and the topology of the FT. Paths starting from the top event to a terminal 1 provide a state in which the top event will occur. These paths are named cut sets.

Figure 2. Binary Decision Diagram (BDD).

ITE (If‐Then‐Else) conditional expression is employed in this research work as an approach for the BDD’s cornerstones, based on the approach presented in reference [30]. Figure 2 shows an example of an ite done in a BDD that is described as: “If event A occurs, Then f1, Else f2” [31]. The solid line always belongs to the ones and the dashed lines to the zeros, explained above.

The following expression is obtained from Figure 2, considering Shannon’s theorem:

, , The size of the BDD, equivalent to CPU runtime, has a strong dependence on the ordering of the

events. Different ranking methods can be used in order to reduce the number of cut sets, and consequently, to reduce the computational runtime. Note that there is no method that provides the minimum size of BDD in all cases. The following methods have been considered in this paper: Top‐down‐left‐right, Depth First Search, AND, Breath First Search, and Level. The AND method has chosen for ranking the events because it provides the best results in this case. For further information about BDDs readers are recommended to see references [20,22,26,27].

The quantitative analysis also takes into account the importance of each basic event within the global system. With this purpose, different importance measures (IMs) are considered in this paper. IMs are used in reliability and risk analysis to quantifying the impact of single component on a system failure [32]. In order to determine the importance of a component, it is necessary to consider all the related basic events as a group [33]. A complete importance analysis of all groups is therefore impractical for large systems, and it is necessary to focus on the most important groups of components [34]. In this work Birnbaum and Criticality IMs are presented.

Birnbaum IM introduced, for an event k, a measure of importance based on the fault probability of the system caused by the failure of the component k [35]. The priority of the event k is given by its Birnbaum IM and is calculated as follows:

where is the failure probability assigned to the k event, and is the probability of the top event. A drawback related to the Birnbaum IM is that it does not consider the failure probability of the k event and, therefore, a high importance can be assigned to rare events.

Criticality IM [18], in contrast to Birnbaum, takes into account the failure probability of a certain component. It rectifies the drawback presented in Birnbaum IM, balancing the values obtained. It is defined as:

where is the Criticality IM of the k event, is the probability assigned to the k event and is the top event probability. Criticality IM provides a different perspective than the Birnbaum IM, even though both are connected providing a measurement of the criticality of each components.

Figure 2. Binary Decision Diagram (BDD).

ITE (If-Then-Else) conditional expression is employed in this research work as an approach forthe BDD’s cornerstones, based on the approach presented in reference [30]. Figure 2 shows an exampleof an ite done in a BDD that is described as: “If event A occurs, Then f 1, Else f 2” [31]. The solid linealways belongs to the ones and the dashed lines to the zeros, explained above.

The following expression is obtained from Figure 2, considering Shannon’s theorem:

f “ bi¨ f1 ` bi¨ f2 “ ite pbi, f1, f2q

The size of the BDD, equivalent to CPU runtime, has a strong dependence on the ordering ofthe events. Different ranking methods can be used in order to reduce the number of cut sets, andconsequently, to reduce the computational runtime. Note that there is no method that providesthe minimum size of BDD in all cases. The following methods have been considered in this paper:Top-down-left-right, Depth First Search, AND, Breath First Search, and Level. The AND method haschosen for ranking the events because it provides the best results in this case. For further informationabout BDDs readers are recommended to see references [20,22,26,27].

The quantitative analysis also takes into account the importance of each basic event withinthe global system. With this purpose, different importance measures (IMs) are considered in thispaper. IMs are used in reliability and risk analysis to quantifying the impact of single componenton a system failure [32]. In order to determine the importance of a component, it is necessary toconsider all the related basic events as a group [33]. A complete importance analysis of all groups istherefore impractical for large systems, and it is necessary to focus on the most important groups ofcomponents [34]. In this work Birnbaum and Criticality IMs are presented.

Birnbaum IM introduced, for an event k, a measure of importance based on the fault probabilityof the system caused by the failure of the component k [35]. The priority of the event k is given by itsBirnbaum IM and is calculated as follows:

IBirnk “BQsysBqk

where qk is the failure probability assigned to the k event, and Qsys is the probability of the top event.A drawback related to the Birnbaum IM is that it does not consider the failure probability of the kevent and, therefore, a high importance can be assigned to rare events.

Criticality IM [18], in contrast to Birnbaum, takes into account the failure probability of a certaincomponent. It rectifies the drawback presented in Birnbaum IM, balancing the values obtained. It isdefined as:

ICritk “qk

Qsys¨BQsysBqk

“ qkQsys

¨ IBirnk

where ICritk is the Criticality IM of the k event, qkis the probability assigned to the k event and Qsys isthe top event probability. Criticality IM provides a different perspective than the Birnbaum IM, even

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though both are connected providing a measurement of the criticality of each components. Therefore,the Criticality IM has been employed in the following sections to carry out a simulation as realisticas possible.

4. FTA for WTs

A study of failure modes and effects analysis (FMEA) for WTs in 2010 (RELIAWIND project)collected the causes of failure and failure modes of a specific WT of 2MW with a diameter of 80m [35]. Some causes of failures (or root causes) are summarized in [36]. These main causes of thefailures can be due to environmental conditions (e.g., lightning, ice, fire, strong winds, etc.) or todefects, malfunctions or failures in the components of the WT (e.g., braking system failure, or bestruck by blade, etc.) [37,38]. The causes of failures (or root causes) of the components of a windturbine can be summarized as follows [35,39]: structural (design fault, external damage, installationdefect, maintenance fault, manufacturing defect, mechanical overload, mechanical overload–collision,mechanical overload–wind, presence of debris); wear (corrosion, excessive brush wear, fatigue,pipe puncture, vibration fatigue, overheating, insufficient lubrication); electrical (calibration error,connection failure, electrical overload, electrical short, insulation failure, lightning strike, loss ofpower input, conducting debris, software design fault). Some of the principal component failuremodes of WTs are [35,39]: mechanical (rupture, uprooting, fracture, detachment, thermal, blockage,misalignment, scuffing); electrical (electrical insulation, electrical failure, output inaccuracy, softwarefault, intermittent output); material (fatigue, structural, ultimate, buckling, deflection).

In this work, the construction of the illustrative FT has been focused on a three blades, pitchsystem and geared WT. The turbine has been divided into four major groups of elements for a betterFTA: The foundation and tower; the blades system; the electrical components (including generator,electrical and electronic components), and; the power train (including speed shafts, bearings and agearbox). The elements of the FT are connected by AND and OR gates, and their fault probability isunknown. The failures considered in this paper are set by an exhaustive review of the literature andthe support of experts from the NIMO and OPTIMUS FP7 European projects [40,41].

Table 1 shows a summary of the failures from the literature taken into account for this paper. Itcan be seen that gearboxes, generators, blades and electric and control systems have been extensivelystudied in the literature, but there are not many references about other components such as brakes,hydraulic and yaw systems.

Table 1. Failures of the main elements of a WT.

Foundation and Tower FailureStructural fault [17,38,42–45]

Yaw system failure [46]

Critical Rotor FailureBlade failure

Structural failure [17,34,47–53]

Pitch system failure [54,55]

Hydraulic system fault [50,56]

Meteorological unit failure [50,57]

Rotor system failure Rotor hub [42,46]

Bearings [45–47]

Power Train Failure

Low speed train failure [17,46,48]

Critical gearbox failure [7,46,53,58–62]

High speed train failure Shaft [6,46,58]

Critical brake failure [6,56]

Electrical Components Failure Critical generator failure [6,46,58,60,63–65]

Power electronics and electric controls failure [17,56,58,60]

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The following sub-sections show the events or components considered to build the FT presentedin Appendix 1. This FT is built from the different sub-trees that correspond to the four main parts of aWT aforementioned (see also the first column of Table 1). The components and faults that are involvedin system failures are obtained from the NIMO and OPTIMUS European Projects. The interrelationbetween these faults is also done considering the literature. The FT in Appendix 1 is composed by thefollowing four main sub-trees:

- g001 corresponds to a “Foundation and Tower Failure” described in Section 4.1.- g002 corresponds to a “Critical Rotor Failure” depicted in Section 4.2.- g003 corresponds to a “Power Train Failure” showed in Section 4.4.- g004 corresponds to a “Electrical Components Failure” presented in Section 4.3.

4.1. Foundation and Tower

The tower supports the nacelle that is located at a suitable height in order to minimize the influenceof turbulence and to maximize the wind energy. The tower is assembled by thin-wall cylindricalelements welded together along their perimeters in three sections that are joined by bolts. This is donein order to enable the transportation of the large structural elements to the wind farm where they needto be assembled [66]. The base section of the tower is installed on a reinforced concrete foundationcomprising a square base [67].

Structural defects associated with the tower, foundation, blades and hub, in the form of fatiguecracks, delamination etc., can initiate and evolve with time [44]. The main causes for structural failuresare fatigue induced crack initiation and propagation, extreme wind speeds and distribution, extremeturbulences, maximum flow inclination and terrain complexity [39], and also the fire, ice accumulationor lightning bolt strikes. Material fatigue [38] (tower-based fatigue damage has been shown to decreasesignificantly when using active pitch for the blades [40,43]), impact of blades on the tower, faultywelding and failure of the brakes [45] are the main representative failure modes.

The literature shows that the major faults found on WT towers are: cracks in the concrete base,corrosion, gaps in the foundation section, loosen studs joining the foundation and the first section,loosen bolts joining first/second and second/third sections and welding damages [38].

On the top of the tower, the yaw system turns the nacelle in an optimum angle with respect to thewind direction. Powered by electrical or hydraulic mechanisms (this paper the electrical is considered),the yaw systems can fail due to the failure of the yaw motor or the meteorological unit [46] resultingin a wrong yaw angle. Structural failures could appear when the yaw motor is damaged or it doesnot have power supply, in addition to extreme wind speed or turbulences and some structural faults.These structural failures can cause the collapse of the tower [38].

4.2. Blade System

The rotor is located inside the nacelle. The blades are attached to the rotor shaft by the huband they are mounted on bearings in the rotor hub. The blades are the components of the WT withthe highest percentage of failures and downtimes [68,69]. Ciang et al. reviewed damage detectionmethods [70] in 2008, considering in particular the blades [42]. The rotor hub supports heavy loadsthat can lead to faults such as clearance loosening at the blade root, imbalance, cracks and surfaceroughness [46]. Bearings between blades and hub can be damaged by wear produced by pitting,deformation of outer face and rolling elements of the bearings [46], spalling and overheating [56].Cracks can appear due to the fatigue [56]. Faults in lubrication and corrosion of pins are typically themain failure cause of bearings.

The blades faults are predominantly related to structural failures, e.g., strength [47] and fatigueof the fibrous composite materials. Other faults, e.g., cracks, erosions, delamination and debonding,could appear in the leading and trailing edges of the blades [48,69]. Delamination and debonding or

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cracks are found in the shell [49,50], and also in the root section of the blades [51]. The tip deflections(a structural failure of the blade [46]) increase drag near the end of the blades [53].

A common fault of the blades is associated with the failure of the pitch control system [54]. Inpitch-controlled turbines, the pitch system is a mechanism that turns the blade, or part of the blade,in order to adjust the angle of attack of the wind. Turbulence of wind is an important cause forpitch system faults [71]. Pitching motion can be done by hydraulic actuators or electric motors. Thehydraulic system leads stiffness of bearings, a little backlash and a higher reliability than the electricmotors [52]. The hydraulic system can suffer from possible defects such as leakages, overpressure andcorrosion [56].

The weather station or meteorological unit provides information about some characteristics ofthe wind (direction and speed) to the control system of the WT. The main failures found in the WTweather station are related to the vane and the anemometer faults [57]. These can be the cause of awrong blade angle [50,55].

4.3. Generator, Electrical and Electronic Components

The generator, electrical and electronic components are installed inside the nacelle. The highspeed shaft drives the rotational torque to the generator, where the mechanical energy is converted toelectrical energy. This conversion needs a specific input speed, or a power electronic equipment toadapt the output energy from the generator to the characteristics of the grid.

Faults in generators can be the result of electrical or mechanical causes [65]. The main electricalfaults are due to open-circuits or short-circuit of the winding in the rotor or stator [58] that could causeoverheating [46]. Many research works have demonstrated that bearings, rotors and stators involvea high failure rate in WTs [63]. The bearing failures of the generator are usually caused by cracks,asymmetry and imbalance [72]. The rotor and stator failures can be produced by broken bars [64],air-gap eccentricities and dynamic eccentricities, among other failures [58]. Rotor imbalance andaerodynamic asymmetry can have their origin in the non-uniform accumulation of ice and dirt overthe blades system [58]. Short-circuit faults, open-circuit faults and gate drive circuit faults are thethree major electrical faults of the power electronics and electric controls in WTs [58]. Corrosion, dirtand terminal damage are the main mechanical defects [56]. The group formed by generator, electricalsystem and control system, has a relevant rate of failures and downtime in WTs.

4.4. Power Train

The power train, or drive train, is installed in the nacelle and is compound by the low speedtrain, the gearbox and the high speed train. Through the main bearing, the rotor is attached to thelow speed shaft that drives the rotational energy to the gearbox. The rotational speed of the rotor isgenerally between 5 and 30 rpm, and the generator speed is from 750 to 1500 rpm, depending on thetype and size of generator. A gearbox is mounted between the rotor and the generator in order toincrease the rotational speeds. The gearbox output is driven to the generator through the high speedtrain. A mechanical brake powered by a hydraulic system is usually mounted in the high speed trainas a secondary safe breaking system.

The low speed train failure includes main bearing [56] and low speed shaft defects. Severevibrations can appear due to impending cracks in any component, or to the mass imbalance in thelow speed shaft [58]. The gearbox failure is one of the most typical failures [53]. There are manystudies about gearboxes in the literature because their failure causes significant downtimes in thesystem [73]. The most common faults were found in gear teeth and bearings due to lubricationfaults [58], e.g., contamination due to defective sealing [54] or loss of oil [60], wear or fatigue damagewhich can generate pitting, cracking, gear eccentricity, gear tooth deterioration, offset or other potentialfaults [46,53].

Overheating can appear in shafts due to the rotational movement of the high speed train. Thewear and fatigue, that can initiate cracks [46] and mass imbalance [58], are the principal source of

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failures in the high speed shaft. The main failure causes of brakes are overpressure or oil leakages [6],cracking of the brake disc and calipers [56].

5. Maintenance Management Approach

The maintenance management proposed in this paper aims to maximise the RAMS of the offshorewind farms optimising the resources such as human or material, conditioned to exogenous variables,e.g., weather conditions [74]. This approach is based on the probability of failure of each WT. Theoperation of the WT will be focused on a set of components collected by a FT (see Appendix 1). Thefault probability of any component is simulated by a statistical function of failure probability over thetime (see Appendix 2). Then, the failure probability of a WT is set by the Boolean expression obtainedfrom the BDD. Therefore, according to the resources, the maintenance task will be done in the WTs thatpresent more fault probability over a threshold set. It will lead to predict any preventive/predictivemaintenance task over the time. The importance measurements will determine the components thatneed a maintenance task. A low probability threshold is set to determine if the fault probability of theWT is under control or not. The importance measurement is calculated with the Criticality IM method.The downtime can be defined as the period of time that is required to carry out the correspondingmaintenance task. Each event of the fault tree has associated one maintenance task with a specificdowntime. The downtime depends on endogenous and exogenous variables. Figure 3 shows theflowchart of the procedure maintenance management.


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The fault probability of any component is simulated by a statistical function of failure probability over the time (see Appendix 2). Then, the failure probability of a WT is set by the Boolean expression obtained from the BDD. Therefore, according to the resources, the maintenance task will be done in the WTs that present more fault probability over a threshold set. It will lead to predict any preventive/predictive maintenance task over the time. The importance measurements will determine the components that need a maintenance task. A low probability threshold is set to determine if the fault probability of the WT is under control or not. The importance measurement is calculated with the Criticality IM method. The downtime can be defined as the period of time that is required to carry out the corresponding maintenance task. Each event of the fault tree has associated one maintenance task with a specific downtime. The downtime depends on endogenous and exogenous variables. Figure 3 shows the flowchart of the procedure maintenance management.

Figure 3. The maintenance management procedure.

6. Case Study

An offshore wind farm composed by 20 WTs has been taken into account. The offshore wind farm has been designed taking into account considerations from expert of the NIMO and OPTIMUS research projects. It has been designed in order to demonstrate and validate the approach proposed in this paper. The WTs are the same type, with the same FT, given in Appendix 1. Different mathematical models have been defined for each event (see Appendix 2). These models have been based on time‐dependent probability functions to describe the behavior of events over the time. These probability models are not intended to match exactly the real behavior of the events because there is no dataset to validate it, therefore it they have been set by the aforementioned expert. For example, the event e006 corresponds to the corrosion of the foundation or tower, where a linear increasing probability have been assigned to this event, this is due to the salinity that is assumed to be constant over the time. The main novelty lies in the procedure to elaborate qualitatively and quantitatively a

Figure 3. The maintenance management procedure.

6. Case Study

An offshore wind farm composed by 20 WTs has been taken into account. The offshore wind farmhas been designed taking into account considerations from expert of the NIMO and OPTIMUS researchprojects. It has been designed in order to demonstrate and validate the approach proposed in this paper.The WTs are the same type, with the same FT, given in Appendix 1. Different mathematical modelshave been defined for each event (see Appendix 2). These models have been based on time-dependentprobability functions to describe the behavior of events over the time. These probability models arenot intended to match exactly the real behavior of the events because there is no dataset to validate it,therefore it they have been set by the aforementioned expert. For example, the event e006 corresponds

Energies 2016, 9, 46 9 of 20

to the corrosion of the foundation or tower, where a linear increasing probability have been assignedto this event, this is due to the salinity that is assumed to be constant over the time. The main noveltylies in the procedure to elaborate qualitatively and quantitatively a preventive maintenance planningprocess based on the knowledge of the WTs and on statistical data that, for example, could be collectedthrough condition monitoring systems [75,76]. The probability functions employed are:

I Constant probability

In this model the probability of the event is constant over the time:

q ptq “ K, pK P R{0 ď K ď 1q

II Exponential increasing probability

In this model, the probability function assigned is:

q ptq “ 1´ e´λt, pλ P R{ λ ě 0q

where λ determines the rising velocity of the probability.III Linear increasing probability

In this model, the probability function is:

q ptq “#

mt mt ă 11 mt ě 1

; @ m ą 1

where m determines the rising velocity of the probability.IV Periodic probability

This model represents those components that need to be replaced, repaired, and zeroed in aperiodical way. In this model, the events have a periodic behavior following the next expression:

q ptq “ 1´ e´λpt´nαq, n “ 1, 2, 3

where λ is a positive parameter and determines the rising velocity of the probability, and α is aparameter that defines the size of the time period.

Figure 4 shows the probability of the events of one WT over the time taken into account theprobability function assigned to each event. The simulation has been carried out for 600 samples,where each sample can be considered as a period of one day. The objective is to propose an algorithmable to collect stochastic information of the failure probability of a complex system.


9

preventive maintenance planning process based on the knowledge of the WTs and on statistical data that, for example, could be collected through condition monitoring systems [75,76]. The probability functions employed are:

I. Constant probability

In this model the probability of the event is constant over the time:

, (K ∈ /0 ≤ K ≤ 1)

II. Exponential increasing probability

In this model, the probability function assigned is:

1 , (λ ∈ / λ 0 where λ determines the rising velocity of the probability. III. Linear increasing probability

In this model, the probability function is:

11 1 ; ∀ 1

where m determines the rising velocity of the probability.

IV. Periodic probability

This model represents those components that need to be replaced, repaired, and zeroed in a periodical way. In this model, the events have a periodic behavior following the next expression:

1 , n = 1, 2, 3 where λ is a positive parameter and determines the rising velocity of the probability, and α is a parameter that defines the size of the time period.

Figure 4 shows the probability of the events of one WT over the time taken into account the probability function assigned to each event. The simulation has been carried out for 600 samples, where each sample can be considered as a period of one day. The objective is to propose an algorithm able to collect stochastic information of the failure probability of a complex system.

Figure 4. Occurrence probabilities of events.

Considering the last probabilities obtained for each event and the analytical expression of the system failure provided by the BDD, the probability of failure for all WTs of the offshore wind farm can be achieved. Figure 5 presents the failure probability of each WT over the time. The probability of failure for each WT is different among them and over the time, because the values of the parameters that represent the occurrence function of each event are not exactly the same.

Figure 4. Occurrence probabilities of events.

Energies 2016, 9, 46 10 of 20

Considering the last probabilities obtained for each event and the analytical expression of thesystem failure provided by the BDD, the probability of failure for all WTs of the offshore wind farmcan be achieved. Figure 5 presents the failure probability of each WT over the time. The probability offailure for each WT is different among them and over the time, because the values of the parametersthat represent the occurrence function of each event are not exactly the same.Energies 2016, 9, 46

10

Figure 5. Probabilities of failure of each WT over the time.

The components that require any maintenance task have been set by the importance measurements, specifically by the Criticality IM method. Figure 6 shows the criticality importance of the events of all WTs considered in this case study in a period of time (in this case the study has been considered for a total of 600 days).

Figure 6. Criticality importance of the events in a given time.

7. Results

The exogenous conditions such as maintenance budget, human and material resources and weather conditions will determine the downtimes, together with the time required to carry out any maintenance task. Figure 7 shows the fault probability over the time of a WT considering different maintenance polices. An upper probability threshold of 0.20 has been established to suggest when the maintenance must be started. Moreover, a lower threshold of 0.15 has been set indicating when the maintenance should be finished. The availability of resources will lead to attend to one or several WTs at the same time.

10

20

30

40

50

60

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90

100

0 510 15

20

0

0.2

0.4

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0.8

1

I. C

ritic

ality

Wind Turbines

Events


The components that require any maintenance task have been set by the importancemeasurements, specifically by the Criticality IM method. Figure 6 shows the criticality importance ofthe events of all WTs considered in this case study in a period of time (in this case the study has beenconsidered for a total of 600 days).


10


The components that require any maintenance task have been set by the importance measurements, specifically by the Criticality IM method. Figure 6 shows the criticality importance of the events of all WTs considered in this case study in a period of time (in this case the study has been considered for a total of 600 days).


7. Results

The exogenous conditions such as maintenance budget, human and material resources and weather conditions will determine the downtimes, together with the time required to carry out any maintenance task. Figure 7 shows the fault probability over the time of a WT considering different maintenance polices. An upper probability threshold of 0.20 has been established to suggest when the maintenance must be started. Moreover, a lower threshold of 0.15 has been set indicating when the maintenance should be finished. The availability of resources will lead to attend to one or several WTs at the same time.

10

20

30

40

50

60

70

80

90

100

0 510 15

20

0

0.2

0.4

0.6

0.8

1

I. C

ritic

ality

Wind Turbines

Events


7. Results

The exogenous conditions such as maintenance budget, human and material resources andweather conditions will determine the downtimes, together with the time required to carry out anymaintenance task. Figure 7 shows the fault probability over the time of a WT considering different

Energies 2016, 9, 46 11 of 20

maintenance polices. An upper probability threshold of 0.20 has been established to suggest when themaintenance must be started. Moreover, a lower threshold of 0.15 has been set indicating when themaintenance should be finished. The availability of resources will lead to attend to one or several WTsat the same time.Energies 2016, 9, 46

11

Figure 7. Probabilities of failure of a WT.

The average fault probability of the offshore wind farm according to the resource employed is illustrated in Figure 8. The probability decreases when the potential of maintenance tasks is bigger. In this case study, the average fault probability of the offshore wind farm decreases faster when it is attended at the same time two instead of one WT, than four instead of three WTs. The main conclusion is that a correct resources use could optimize the average fault probability of the offshore wind farm.

Figure 8. Average fault probability of the offshore wind farm.

The boxplots of Figure 9 show the behavior of the offshore wind farm for different maintenance management policies. The approach lead to control the average probability of failure by a correct maintenance police, and the boxes to be smaller, i.e., presenting a homogeneous probability distribution in all WTs.

The maintenance management performance for offshore wind farms is subject to several uncertainties related to the randomness of exogenous conditions, e.g., weather conditions [77]. Therefore, the approach presented requires weather forecasting. Weather forecasting depends on the temperature, dew point, wind velocity, pressure, visibility, cloud height and quantity [4]. In addition, the state of the sea, the wind and the wave heights need to be considered. There are some probabilistic models based on historical wave height data that are used to determine the conditions of the sea in a certain moment, e.g., the Markovian wave height model [78], forecasting of safe sea‐state using finite elements method and artificial neural networks [79], short‐term predictions based on nonlinear deterministic time series analysis [80], Gaussian processes [81], resampling methods, parametric models, etc.


The average fault probability of the offshore wind farm according to the resource employed isillustrated in Figure 8. The probability decreases when the potential of maintenance tasks is bigger.In this case study, the average fault probability of the offshore wind farm decreases faster when it isattended at the same time two instead of one WT, than four instead of three WTs. The main conclusionis that a correct resources use could optimize the average fault probability of the offshore wind farm.


11


The average fault probability of the offshore wind farm according to the resource employed is illustrated in Figure 8. The probability decreases when the potential of maintenance tasks is bigger. In this case study, the average fault probability of the offshore wind farm decreases faster when it is attended at the same time two instead of one WT, than four instead of three WTs. The main conclusion is that a correct resources use could optimize the average fault probability of the offshore wind farm.


The boxplots of Figure 9 show the behavior of the offshore wind farm for different maintenance management policies. The approach lead to control the average probability of failure by a correct maintenance police, and the boxes to be smaller, i.e., presenting a homogeneous probability distribution in all WTs.

The maintenance management performance for offshore wind farms is subject to several uncertainties related to the randomness of exogenous conditions, e.g., weather conditions [77]. Therefore, the approach presented requires weather forecasting. Weather forecasting depends on the temperature, dew point, wind velocity, pressure, visibility, cloud height and quantity [4]. In addition, the state of the sea, the wind and the wave heights need to be considered. There are some probabilistic models based on historical wave height data that are used to determine the conditions of the sea in a certain moment, e.g., the Markovian wave height model [78], forecasting of safe sea‐state using finite elements method and artificial neural networks [79], short‐term predictions based on nonlinear deterministic time series analysis [80], Gaussian processes [81], resampling methods, parametric models, etc.


The boxplots of Figure 9 show the behavior of the offshore wind farm for different maintenancemanagement policies. The approach lead to control the average probability of failure by a correctmaintenance police, and the boxes to be smaller, i.e., presenting a homogeneous probability distributionin all WTs.

The maintenance management performance for offshore wind farms is subject to severaluncertainties related to the randomness of exogenous conditions, e.g., weather conditions [77].Therefore, the approach presented requires weather forecasting. Weather forecasting depends on thetemperature, dew point, wind velocity, pressure, visibility, cloud height and quantity [4]. In addition,

Energies 2016, 9, 46 12 of 20

the state of the sea, the wind and the wave heights need to be considered. There are some probabilisticmodels based on historical wave height data that are used to determine the conditions of the sea ina certain moment, e.g., the Markovian wave height model [78], forecasting of safe sea-state usingfinite elements method and artificial neural networks [79], short-term predictions based on nonlineardeterministic time series analysis [80], Gaussian processes [81], resampling methods, parametricmodels, etc.Energies 2016, 9, 46

12

Figure 9. Boxplot of the fault probability of the offshore wind farm for WT operated at the same time.

The maintenance task will be carried out when certain permission value is reached. This dimensionless value, which varies from 0 to 1, will be given by a weighting of the weather conditions and external permissions. It has been simulated in this paper and validated by experts. Figure 10 shows the maximum allowed value assigned to each event. The maximum allowed valued is randomly generated for this case. It is due to the goal of this study is to clarify how the proposed methodology should be applied, taking into account that the method is close to the reality only from the qualitative point of view. This value is compared with a predicted value given randomly in this paper in order to consider the stochastic of the system. If the value assigned to the task is bigger than the predicted value, the maintenance task must be carried out, in other case, it must be necessary to wait for a suitable value from the forecasting.

Figure 10. Maximum allowed exogenous pondered value for each maintenance tasks.

Figure 11 shows a randomized forecasting value of the weather conditions given for each day (sample) evaluated in the example. This figure can be used to determine the tasks that can be performed according to the exogenous variables. For example, in the 100th day (green circle) there is a value of 0.2 (this value is a ponderation between temperature, dew point, wind velocity, pressure, visibility, etc.), i.e., any maintenance task can be carried out because this value is lower than all the maximum allowed exogenous pondered values. However, in the 300th day (red circle) none of the tasks can be carried out because the value is higher than the allowable value in all the cases.

1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829

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The maintenance task will be carried out when certain permission value is reached. Thisdimensionless value, which varies from 0 to 1, will be given by a weighting of the weather conditionsand external permissions. It has been simulated in this paper and validated by experts. Figure 10shows the maximum allowed value assigned to each event. The maximum allowed valued is randomlygenerated for this case. It is due to the goal of this study is to clarify how the proposed methodologyshould be applied, taking into account that the method is close to the reality only from the qualitativepoint of view. This value is compared with a predicted value given randomly in this paper in orderto consider the stochastic of the system. If the value assigned to the task is bigger than the predictedvalue, the maintenance task must be carried out, in other case, it must be necessary to wait for asuitable value from the forecasting.


12


The maintenance task will be carried out when certain permission value is reached. This dimensionless value, which varies from 0 to 1, will be given by a weighting of the weather conditions and external permissions. It has been simulated in this paper and validated by experts. Figure 10 shows the maximum allowed value assigned to each event. The maximum allowed valued is randomly generated for this case. It is due to the goal of this study is to clarify how the proposed methodology should be applied, taking into account that the method is close to the reality only from the qualitative point of view. This value is compared with a predicted value given randomly in this paper in order to consider the stochastic of the system. If the value assigned to the task is bigger than the predicted value, the maintenance task must be carried out, in other case, it must be necessary to wait for a suitable value from the forecasting.


Figure 11 shows a randomized forecasting value of the weather conditions given for each day (sample) evaluated in the example. This figure can be used to determine the tasks that can be performed according to the exogenous variables. For example, in the 100th day (green circle) there is a value of 0.2 (this value is a ponderation between temperature, dew point, wind velocity, pressure, visibility, etc.), i.e., any maintenance task can be carried out because this value is lower than all the maximum allowed exogenous pondered values. However, in the 300th day (red circle) none of the tasks can be carried out because the value is higher than the allowable value in all the cases.

1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829

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Figure 11 shows a randomized forecasting value of the weather conditions given for each day(sample) evaluated in the example. This figure can be used to determine the tasks that can be performedaccording to the exogenous variables. For example, in the 100th day (green circle) there is a value of0.2 (this value is a ponderation between temperature, dew point, wind velocity, pressure, visibility,

Energies 2016, 9, 46 13 of 20

etc.), i.e., any maintenance task can be carried out because this value is lower than all the maximumallowed exogenous pondered values. However, in the 300th day (red circle) none of the tasks can becarried out because the value is higher than the allowable value in all the cases.Energies 2016, 9, 46

13

Figure 11. Representative exogenous pondered value forecasting per day.

Figure 12 represents the weather influence on the distribution of the failure probabilities of the WTs over the time. Different weather scenarios have been taken into account randomly in order to evaluate the weather conditions and the influence to the maintenance tasks.

Figure 12. Influence of exogenous variables on the state of the offshore wind farm.

In the top boxplot of Figure 12, the weather conditions have not been taken into account. In the second one, the weather forecasting presented in Figure 11 has been considered. In the last one boxplot, an adverse weather conditions have been established. The presence of adverse weather conditions makes to increase the average fault probability of the offshore wind farm, and the size of the boxes of boxplot decreases because the maintenance tasks that can be done are minimum.

8. Conclusions

The offshore wind energy is being supported by the international community. Offshore wind farms employ large and complex wind turbines that generate more power electricity than onshore. The farms are located in places with difficulty to access that depends of the weather conditions. These conditions have leaded the development of robust remote condition monitoring system in order to increase the RAMS of the offshore wind farms.

This paper presents the BDD in order to evaluate qualitatively the FTA of a WT. The approach is based on the fault probabilities of each component of the WT, that depend of a statistical function of probability of occurrence over the time. The fault probability of the WT has been set by the Boolean

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

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Figure 12 represents the weather influence on the distribution of the failure probabilities of theWTs over the time. Different weather scenarios have been taken into account randomly in order toevaluate the weather conditions and the influence to the maintenance tasks.


13


Figure 12 represents the weather influence on the distribution of the failure probabilities of the WTs over the time. Different weather scenarios have been taken into account randomly in order to evaluate the weather conditions and the influence to the maintenance tasks.


In the top boxplot of Figure 12, the weather conditions have not been taken into account. In the second one, the weather forecasting presented in Figure 11 has been considered. In the last one boxplot, an adverse weather conditions have been established. The presence of adverse weather conditions makes to increase the average fault probability of the offshore wind farm, and the size of the boxes of boxplot decreases because the maintenance tasks that can be done are minimum.

8. Conclusions

The offshore wind energy is being supported by the international community. Offshore wind farms employ large and complex wind turbines that generate more power electricity than onshore. The farms are located in places with difficulty to access that depends of the weather conditions. These conditions have leaded the development of robust remote condition monitoring system in order to increase the RAMS of the offshore wind farms.

This paper presents the BDD in order to evaluate qualitatively the FTA of a WT. The approach is based on the fault probabilities of each component of the WT, that depend of a statistical function of probability of occurrence over the time. The fault probability of the WT has been set by the Boolean

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

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In the top boxplot of Figure 12, the weather conditions have not been taken into account. In thesecond one, the weather forecasting presented in Figure 11 has been considered. In the last one boxplot,an adverse weather conditions have been established. The presence of adverse weather conditionsmakes to increase the average fault probability of the offshore wind farm, and the size of the boxes ofboxplot decreases because the maintenance tasks that can be done are minimum.

8. Conclusions

The offshore wind energy is being supported by the international community. Offshore windfarms employ large and complex wind turbines that generate more power electricity than onshore.The farms are located in places with difficulty to access that depends of the weather conditions. Theseconditions have leaded the development of robust remote condition monitoring system in order toincrease the RAMS of the offshore wind farms.

This paper presents the BDD in order to evaluate qualitatively the FTA of a WT. The approach isbased on the fault probabilities of each component of the WT, that depend of a statistical function of

Energies 2016, 9, 46 14 of 20

probability of occurrence over the time. The fault probability of the WT has been set by the Booleanexpression obtained by the BDD. An optimal ranking of the events has been done for minimising thecomputational cost.

The IMs have been employed in order to facilitate the improvement of the maintenancemanagement and the resources deployment in an offshore wind farm, where a proper and accurateprioritization of the basic events has been elaborated according to Criticality IM method.

The maintenance management approach proposed in this paper maximise the RAMS of theoffshore wind farm, optimising the resources as human, materials, etc. The maintenance task will becarried out in the WTs that present more fault probability over a threshold. It will lead to establishmentof preventive/predictive maintenance tasks over time. A low probability threshold has also been set todetermine when the fault probability of the WT is under control. The time to carry out a maintenancetask has been established by the downtime associated to each failure. The downtime depends on thetime to repair or replace the component, human resourcesstate of the sea, etc.

It has been demonstrated that the average fault probability of the offshore wind farm decreasesmore when two instead of one WT can be attended at the same time than between four instead of three.The main conclusion is that there is a reasonable amount of resources that allow controlling the averagefault probability of the offshore wind farm, and this method can be used to calculate this value.

The weather conditions have been also considered. The average fault probability of the offshorewind farm increases when there is a presence of adverse weather conditions. The adverse weatherincreases the gap between the failure probabilities of the different WTs that compose the wind farmbecause the maintenance tasks that can be done are minimum.

The dynamic analysis proposed in this paper can be used to improve the maintenance planningusing the fault probability of the system over the time. The fault probability and the IMs determinewhen the maintenance tasks must be carried out and to set the tasks over the events.

The qualitative data used in this paper is gathered from several research projects and the resultshave been validated by experts involve in the research projects. The main novelty of the paper is theprocedure to analyse endogenous and exogenous data using graphical tools.

Acknowledgments: The work reported herewith has been financially supported by the European Commissionunder the European FP7 OPTIMUS project [41], and the Spanish Ministerio de Economía y Competitividad, underResearch Grant DPI2012-31579.

Author Contributions: Alberto Pliego, Fausto García and Jesús Pinar conceived and designed the experiments;Alberto Pliego, Fausto García and Jesús Pinar performed the experiments; Alberto Pliego, Fausto García andJesús Pinar analyzed the data Alberto Pliego, Fausto García and Jesús Pinar contributed reagents/materials/analysis tools; Alberto Pliego, Fausto García and Jesús Pinar wrote the paper.

Conflicts of Interest: The authors declare no conflict of interest.

Appendix 1. FT for a Wind Turbine


14

expression obtained by the BDD. An optimal ranking of the events has been done for minimising the computational cost.

The IMs have been employed in order to facilitate the improvement of the maintenance management and the resources deployment in an offshore wind farm, where a proper and accurate prioritization of the basic events has been elaborated according to Criticality IM method.

The maintenance management approach proposed in this paper maximise the RAMS of the offshore wind farm, optimising the resources as human, materials, etc. The maintenance task will be carried out in the WTs that present more fault probability over a threshold. It will lead to establishment of preventive/predictive maintenance tasks over time. A low probability threshold has also been set to determine when the fault probability of the WT is under control. The time to carry out a maintenance task has been established by the downtime associated to each failure. The downtime depends on the time to repair or replace the component, human resources, state of the sea, etc.

It has been demonstrated that the average fault probability of the offshore wind farm decreases more when two instead of one WT can be attended at the same time than between four instead of three. The main conclusion is that there is a reasonable amount of resources that allow controlling the average fault probability of the offshore wind farm, and this method can be used to calculate this value.

The weather conditions have been also considered. The average fault probability of the offshore wind farm increases when there is a presence of adverse weather conditions. The adverse weather increases the gap between the failure probabilities of the different WTs that compose the wind farm because the maintenance tasks that can be done are minimum.

The dynamic analysis proposed in this paper can be used to improve the maintenance planning using the fault probability of the system over the time. The fault probability and the IMs determine when the maintenance tasks must be carried out and to set the tasks over the events.

The qualitative data used in this paper is gathered from several research projects and the results have been validated by experts involve in the research projects. The main novelty of the paper is the procedure to analyse endogenous and exogenous data using graphical tools.

Acknowledgments: The work reported herewith has been financially supported by the European Commission under the European FP7 OPTIMUS project [41], and the Spanish Ministerio de Economía y Competitividad, under Research Grant DPI2012‐31579.

Author Contributions: Alberto Pliego, Fausto García and Jesús Pinar conceived and designed the experiments; Alberto Pliego, Fausto García and Jesús Pinar performed the experiments; Alberto Pliego, Fausto García and Jesús Pinar analyzed the data Alberto Pliego, Fausto García and Jesús Pinar contributed reagents/materials/analysis tools; Alberto Pliego, Fausto García and Jesús Pinar wrote the paper.

Conflicts of Interest: The authors declare no conflict of interest.

Appendix 1. FT for a Wind Turbine TOP

g014

g005

g001

g061

g052

g064

g058

g054

e003

e005 e006 e007 e008

e093

g068

e105e104

e077

e082 e083 g059

e090

e089

e088

e091

e009e004

g002

g027 g028

e037g029

g015

e016

e033

g022 g023 g024

e026 e027 e028 e029 e030

e031 e032

e034 e035

e025e038 e039 e040 e041

e045e044e043

g030

e046 e047

g004

g046

e066g049

e068 e069 e070

g060

e095g063

e096 e097 e098 e100

g050

g051

e074 e075 e076e071 e099

e101

e093e087

g055

e086

e073

e094

e072

e067

g053

g056

e078 e079 e080 e081

g032

e059 e060 e061 e062 e063 e064

g031

g038

g040

e056e055

e054e053

e057

g037

e050 e051

e058

e052e049

g033 g034

g036

g042g041

e042g020

e023e022

g011

e011e010

g025

g043g045

e024g021g017

e020 e021e019

e017g019 e017

g018

e085 g057

g008

e002g012

g009

g039

e048

g067

g065g062 e092

g003

e018

g016

g026e036

e048

g035

e065g048

g047

e065

e102

g066

e103

e001

g007

e003

e012g010

g006

e014e013

g013

e015

g044

e084

Energies 2016, 9, 46 15 of 20

Appendix 2. Events and Probabilistic Models

Fault Tree 1 Foundation and Tower Failure Probabilistic ModelAssignment

Intermediate Event Code Final Event Code

Yaw System Failure g005 Yaw motor fault e001 ConstantCritical Structural Failure g006 Abnormal Vibration I e002 Linear Increasing

yaw motor failure g007 Abnormal Vibration H e003 Linear IncreasingWrong Yaw Angle g008 Cracks in concrete base e004 Constant

Structural Failure(Foundation and tower) g009

Welding damagee005

Constant

No electric power foryaw motor

g010 Corrosion e006 Linear Increasing

Metereologhical Unit Failure g011Loosen studs in joining foundation

and first sectione007 Linear Increasing

Structural Fault(Foundation and tower)

g012Loosen bolts in joining

different sectionse008 Linear Increasing

Gaps in the foundation section e009 Exponential IncreasingVane damage e010 Exponential Increasing

Anemometer damage e011 Exponential IncreasingHigh wind speed e012 Periodic

No power supply from generator e013 ConstantNo power supply from grid e014 Constant

Fault Tree 2 Critical Rotor Failure Probabilistic ModelAssignment

Intermediate Event Code Final Event Code

Critical blade failure g013 High wind speed e015 PeriodicBlade Failure g014 Blade Angle asymmetry e016 Exponential Increasing

Pitch System Failure g015 Abnormal Vibration A e017 Exponential IncreasingCritical structuralFailure (Blades)

g016 Motor failure e018 Exponential Increasing

Hydraulic system Failure g017 Leakages e019 ConstantWrong Blade Angle g018 Over pressure e020 Constant

Hydraulic system Fault g019 Corrosion e021 Exponential IncreasingMetereologhical Unit Failure g020 Vane damage e022 Constant

Structural Failure (Blades) g021 Anemometer damage e023 ConstantLeading and traililling edges g022 Abnormal Vibration B e024 Constant

Shell g023 Root Cracks e025 ConstantTip g024 Cracks e026 Constant

Rotor System Failure g025 Erosion e027 Exponential Increasing

Rotor System Fault g026Delamination in leading

edges of bladese028 Exponential Increasing

Bearings (Rotor) g027Delamination in trailing

edges of bladese029 Exponential Increasing

Rotor Hub g028 Debonding in edges of blades e030 Exponential IncreasingWear g029 Delamination in shell e031 Exponential Increasing

Imbalance g030 Crack with structural damage e032 ConstantCrack on the beam-shell joint e033 Constant

Open tip e034 ConstantLightning strike e035 Periodic

Abnormal Vibration C e036 ConstantCracks e037 Constant

Corrosion of Pins e038 Exponential IncreasingAbrasive Wear e039 Exponential Increasing

Pitting e040 Linear IncreasingDeformation of face & rolling element e041 Linear Increasing

Lubrication Fault e042 Linear IncreasingClearance loosening at root e043 Exponential Increasing

Cracks e044 ConstantSurface Roughness e045 Constant

Mass Imbalance e046 Exponential IncreasingFault in Pitch adjustment e047 Exponential Increasing

Energies 2016, 9, 46 16 of 20

Appendix 2. Cont.

Fault Tree 3 Electrical Components Failure Probabilistic ModelAssignmentIntermediate Event Code Final Event Code

Critical Generator Failure g031 Abnormal Vibration G e048 Exponential Increasing

Power Electronics and ElectricControls Failure

g032 Cracks e049 Constant

Mechanical Failure(Generator)

g033 Imbalance e050 Exponential Increasing

Electrical Failure (Generator) g034 Asymmetry e051 Exponential IncreasingBearing Generator Failure g035 Air-Gap eccentricities e052 Linear IncreasingRotor and Stator Failure g036 Broken bars e053 Linear IncreasingBearing Generator Fault g037 Dynamic eccentricity e054 Linear IncreasingRotor and Stator Fault g038 Sensor T error e055 constantAbnormal Signals A g039 T above limit e056 Periodic

Overwarming generator g040 Short Circuit (Gen) e057 ConstantElectrical Fault (PE) g041 Open Circuit (Gen) e058 Constant

Mechanical Fault (PE) g042 Short Circuit e059 ConstantOpen Circuit e060 Constant

Gate drive circuit e061 linear increasingCorrosion e062 Periodic

Dirt e063 PeriodicTerminals damage e064 linear increasing

Fault Tree 4 Power Train Failure Probabilistic ModelAssignmentIntermediate Event Code Final Event Code

Low speed train Failure g043 Abnormal Vibration D e065 ConstantCritical Gearbox Failure g044 Cracks in main bearing e066 ConstantHigh speed train Failure g045 Spalling e067 Linear Increasing

Main Bearing failure g046 Corrosion of Pins e068 Linear IncreasingLow speed shaft failure g047 Abrasive Wear e069 Constant

Main Bearing fault g048 Deformation of face & rolling element e070 Linear IncreasingWear main bearing g049 Pitting e071 exponential increasing

Low speed shaft fault g050 Imbalance e072 ConstantWear low shaft g051 Cracks in l.s. shaft e073 Linear IncreasingGearbox Fault g052 Spalling e074 Constant

Bearings failure(Gearbox) g053 Abrasive Wear e075 ConstantLubrication fault g054 Pitting e076 Constant

Gear Failure g055 Abnormal Vibration F e077 Linear IncreasingWear bearing gearbox g056 Corrosion of Pins e078 Exponential Increasing

Gear Fault g057 Abrasive Wear e079 Linear IncreasingTooth Wear g058 Pitting e080 Constant

Offset g059 Deformation of face & rolling element e081 Linear IncreasingHigh speed shaft Failure g060 Oil Filtration e082 Constant

Critical Brake Failure g061 Particle Contamination e083 Exponential IncreasingHigh speed structural damage g062 Overwarming gearbox e084 Linear Increasing

Wear high shaft g063 Abnormal Vibration E e085 PeriodicBrake Fault g064 Eccentricity e086 Constant

Abnormal Signals B g065 Pitting e087 Linear IncreasingHydraulic brake system Fault g066 Cracks in gears e088 Exponential Increasing

Abnormal Signals C g067 Gear tooth deterioration e089 Exponential IncreasingOverwarming brake g068 Poor design e090 Periodic

Tooth surface defects e091 ConstantAbnormal Vibration J e092 Constant

Cracks in h.s. shaft e093 Linear IncreasingImbalance e094 Periodic

Overwarming e095 Exponential IncreasingSpalling e096 Constant

Abrasive Wear e097 Linear IncreasingPitting e098 Constant

Cracks in brake disk e099 Exponential IncreasingMotor brake fault e100 Constant

Oil Leakage e101 Linear IncreasingOver pressure e102 Constant

Abnormal speed e103 Linear IncreasingT sensor error e104 PeriodicT above limit e105 Periodic

Energies 2016, 9, 46 17 of 20

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